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physica status solidi (b)

Theory of the lineshape of quantum well intersubband transitions: optical dephasing and light propagation effects

I. Waldmüller, Michael Woerner, Jens Förstner, Andreas Knorr

Published Jul 21, 2003• 19 citations
Publisher

Abstract

Abstract We outline a theoretical description of the absorption linewidth of quantum well intersubband transitions by solving Maxwell's equations for a non‐local susceptibility including many particle effects. We show that the intersubband absorption results from a complex interplay between mean‐field effects, dephasing contributions and light propagation effects, all being very sensitive to subband dispersion.

DOI
10.1002/pssb.200303165

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Abstract We outline a theoretical description of the absorption linewidth of quantum well intersubband transitions by solving Maxwell's equations for a non‐local susceptibility including many particle effects. We show that the intersubband absorption results from a complex interplay between mean‐field effects, dephasing contributions and light propagation effects, all being very sensitive to subband dispersion.
Infrared intersubband optical absorption between the quantized subbands and the Stark effects is of considerable interest because of their potential applications in high-speed IR modulators and photodetectors. Recently, we calculated the linear1 and third-order nonlinear2 intersubband optical absorptions with an applied electric field for the infinite quantum-well model with an effective well width (which gives the same ground state energy of a given finite quantum well). The observed intersubband absorption has a large dipole strength suggesting large optical nonlinearities which are in good agreement with our calculation based on the simple model. Distinct features of the intersubband absorption are as follows: (a) The absorption peak for the intersubband absorption increases in energy with increasing electric field over a wide range of the electric field because the energy difference between the two lowest subbands increases with the electric field. (b) The absorption peak for the intersubband absorption may (1) increase in magnitude with an increasing electric field if the intrasubband relaxation time τin is assumed to be constant or (2) decrease with an increasing electric field if the field broadening of the linewidth is taken into account. The nonlinear optical absorption coefficient with the electric field dependence is discussed.
Taking as a starting point the Liouville equation for the one-body density matrix operator, a general expression for the third-order nonlinear current density responsible for the optical Kerr effect associated with intersubband transitions in a quantum well is derived by use of the perturbative expansion method. The nonlinear current density is related to the local field inside the quantum well via a nonlocal relation. By combining the field-induced nonlinear part of the current density with the Maxwell equation, a nonlinear integral equation for the local field is established. For a two-level quantum well, the integral equation is solved exactly. The nonlinear optical reflectivity, transmittance, and absorbance of the quantum well in turn are obtained. Numerical calculations of the light-induced change of the optical spectra are presented for a Al 0.5 Ga 0.5 As/GaAs/Al 0.5 Ga 0.5 As quantum well. The numerical results show that the optical reflectivity and absorbance decrease, and the transmittance increases as the optical intensity of the incident light is increased. In the case where the quantum-well structure is heavily doped, a notable light-induced red-shift of the location of the resonance peak in the optical spectra stemming from the combined local-field effect and field-induced population redistribution is predicted.
In this article, we have investigated the optical properties of intersubband transitions in an asymmetric AlGaAs/GaAs coupled quantum wells system. We solved the Schrödinger equation numerically using homemade finite difference codes to determine the electronic structure. The susceptibilities were calculated in frame of density matrix equations. The effect of relative phase variation between applied fields, on the linear absorption coefficients, relative refractive index changes, and group velocity has been investigated. The results show that the linear optical properties are extremely phase-dependent. By adjusting the phase, it is possible to obtain absorption curves with dispersion-like profile and vice versa.
The effect of the depolarization field on the nonlinear intersubband absorption spectrum of a rectangular quantum well (described by the two-subband model) is discussed. Calculations are performed in the framework of the density-matrix formulation with use of the relaxation-time approximation. Obtained results show that the depolarization effect not only shifts the peak by an amount depending on the intensity of the incident light but also leads to a significant distortion (asymmetry) of the line shape.
Radiative coupling of resonantly excited intersubband transitions in GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs multiple quantum wells can have a strong impact on the coherent nonlinear optical response, as is shown by phase and amplitude resolved propagation studies of ultrashort electric field transients. Upon increasing the driving field amplitude, strong radiative coupling leads to a pronounced self-induced absorption, followed by a bleaching due to the onset of delayed Rabi oscillations. A many-particle theory including light propagation effects accounts fully for the experimental results.
Summary form only given. Several characteristic features have attracted the current interest in nonlinear optical phenomena of quantum well-intersubband transitions (QWISBTs): the ability to design the quantum well structure and hence control the transition energies and optical dipole matrix elements; the almost equal effective masses of the subbands leading to virtually discrete optical transitions; and the weak localization of electrons in the conduction band leading to large optical dipole matrix elements and hence strong optical interactions.